Simulate sound waves (physics)?
Can Blender be used to simulate the transmission of sound waves
  through a medium (most likely air)?


No, blender is designed to create images and animations (including soft and rigid body physics) which may include sounds, having that said blender copes with light not with audio.

The only support for audio (besides playback) I'm aware is to bake the amplitude (volume) of a distinct frequency range to an f-curve.

These f-curves could be used to animate an object in an animation like the vibrations of strings, or to visualize sounds like a spectrum analyzer does (scaling boxes).

Tutorial here

IMHO The best would be to play around with these possibities and evaluate the options provided and in case blender is still a candidate (for your project) too ask a more specific question.